\newproblem{lay:2_9_19}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.9.19}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  If the subspace of all solutions of $A\mathbf{x}=\mathbf{0}$ has a basis consisting of 3 vectors and if $A$ is a $5\times 7$ matrix, what is the
	rank of $A$.
}{
  % Solution
	According to the rank theorem
	\begin{center}
		$\mathrm{Rank}\{A\}+\mathrm{dim}\{\mathrm{Nul}\{A\}\}=n$
	\end{center}
	where $n$ is the number of columns of $A$. In this particular case,
	\begin{center}
		$\mathrm{Rank}\{A\}+3=7 \Rightarrow \mathrm{Rank}\{A\}=4$
	\end{center}
}
\useproblem{lay:2_9_19}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
